How can I map a texture node, using a factor similar to pointiness, when the mesh edges are too rounded?
I would use the normal output of the texture coordinate node and remap the values with a rgb curves node. 

For this you need to have your model's normals pointing in a global direction. Say you modeled the body along the XY plane, so the normals of the part where the cord is (I don't know the technical term) points towards the Z direction.

So we will create a gradient from blackish to orange-ish along the mesh, depending on the value of the normal. A Z component of Z means black values, and a Z component of 1 (pointing UP) is more red.

We will add a noise texture to make it a little bit more believable, but I think you know how to do this already.

The node network :



Zoom on the "RGB curves" node :



Result :